Roger Tilton had been wrestling with his conscience for five months by the time he stood up on the gymnasium floor of a college in New Hampshire and confronted Hillary Clinton.

"I have two daughters and they both want me to vote for you as president," he began. His friends supported Clinton. "They say that you are warm and sincere and funny, smart, brilliant, intelligent." But Tilton, a financial adviser, was torn. "I like your programmes but there is still a disconnect for me, he said. "Sometimes I think you come on cold and politically calculating."

He added: "There is a disconnect."

Clinton's smile stayed fixed, but her jaw clenched slightly. "Well your two daughters sound very smart to me," she said. She ran through her CV and her standard complaint that she is judged far more harshly than others in the race for the White House. "I can't be anything other than what I am. I'll do the very best I can," Clinton said.

Tilton was unconvinced and in that exchange - a not untypical encounter for Clinton as she campaigns in New Hampshire and Iowa - lies the dilemma confronting many Democratic activists.

They respect Clinton's intellect. They admire her performance in the debates. They realise she has grown into a formidable candidate. But it is difficult for them to commit to a candidate who not only voted in favour of the war on Iraq in 2002, but has refused to express contrition, or any deep emotion, about that choice. The unease is deepened by Clinton's vote last September for designating Iran's Revolutionary Guards a terrorist entity.

That frustration with Clinton now threatens her chances of winning the Democratic nomination. With just 12 days to go before the Iowa caucuses on January 3 and the start of the primary season, Clinton has made a strategic shift in her campaign to try to persuade reluctant voters to like her and trust her.

It's a tough fight. Opinion polls in Iowa show Clinton in a dead heat with Barack Obama and John Edwards. Some Democratic county officials predict Clinton could be relegated to third place, a finish that could damage her in the New Hampshire primary five days later, and ultimately cost her the nomination.

The new Clinton, as revealed during the last week in Iowa and New Hampshire, is a very different woman than the cerebral creature who first hit the campaign trail. "It has moved much more towards a 'please like me' kind of pitch," said David Redlawsk, who teaches politics at the University of Iowa and is the director of its Hawkeye poll. "I think it's an effort to stem a perceived drop in support among women."

That's the public stage. Behind the scenes, campaign operatives have been waging a ruthless smear campaign against Obama and, to a lesser extent, Edwards. In recent days, Clinton aides have tried to raise doubts about Obama's overweening ambition (he wanted to be president when he in kindergarten); his character (he tried drugs when he was a teenager); his commitment to principle (in the Illinois senate he frequently voted "present" to avoid taking sides on an issue); and, within the past 24 hours, his knowledge of world affairs.

So far as the people of Iowa and New Hampshire are concerned, however, the campaign wants their eyes fixed on positive images of Clinton as daughter, mother, and friend.

In one campaign ad, Dorothy Rodham, 88, confides she would vote for Clinton even if she wasn't her daughter, saying "she has empathy for other people's unfortunate circumstances".

Other ads show Clinton sharing a joke with her daughter, Chelsea, and wrapping presents, such as universal healthcare, for voters: Clinton as Santa.

In election meetings, she is introduced by ordinary people offering up examples of everyday kindness - "the Hillary I know". Clinton is making herself more available for questions; she has gone canvassing door-to-door in a working-class neighbourhood of Manchester, New Hampshire.

All of this effort is aimed at winning back the women who have drifted from Clinton during the past six weeks. The most recent polls suggest that Obama has caught up to Clinton and eliminated her advantage among women voters.

Many defected for reasons like Tilton's - they just don't trust her. Anne Seltzer, an Iowa pollster, argues that women expect more candour from candidates. "There are questions of manipulation and secrecy and that is a real problem for women, who tend to be appreciative of frankness," she said.

Some women admit it was painful to realise they may not vote for Clinton. "I used to say to people that whenever a woman runs for president - even if it's Elizabeth Dole [who ran for the Republican nomination in 2000] - I used to say I've got to do it," said Laurie Moore, who works in the education department at Iowa State University. "I'm thinking more carefully about it now ... Maybe it's Hillary, and maybe it isn't but I don't think that just because she is a woman automatically warrants my support."

Clinton started her campaign last January with a nearly two-to-one advantage in support from women. She performed especially well among lower-income women, those without a college education, and women in their 50s and up.

The campaign moved to exploit that advantage. There were Moms for Hillary and block parties for Club 44 - another women's group patronised by Geraldine Ferraro, the Democratic vice-presidential candidate in 1984, and Madeleine Albright, the former secretary of state. For Iowans, there was the website yougogirl.com offering advice to newcomers about the caucus system, and the now requisite house parties.

Clinton also had what was presumed to be an invincible political machine. She had strategists, pollsters and field organisers whom she had known since her husband's run for the White House in 1992. In terms of presidential politics, this campaign is the fifth generation.

But the Clinton machine was not built for Iowa, where the state's lead in the primary calendar has produced a breed of voter that expects and demands personal attention. Bill Clinton bypassed the state in 1992 because Iowa senator Tom Harkin was running and the southern governor figured he had no chance against a local. Some on his wife's staff thought she should skip Iowa as well.

Instead, Clinton figured her best strategy was to campaign almost as if she was already the Democratic nominee. She played it safe, sticking to carefully controlled situations. Although Clinton made several trips to Iowa over the summer - including the state fair in August that has become a ritual for candidates - the campaign offered few opportunities for Iowans to really get to know her.

Clinton was happy to pose for photographs flipping pork chops on a grill, but she was just not available to Iowans for conversations about her political beliefs, or what she might do as president. In her election meetings, Clinton typically took three questions from the floor; Edwards averaged closer to 10. Clinton went for weeks at a time without holding a single press conference; some candidates hold three or four a day.

The campaign also initially failed to calibrate their message to voters who pride themselves on making informed decisions. Eileen Willingham, a Spanish translator in Iowa City, was turned off Clinton when she attended a house party for women voters in October.

"I found it anti-intellectual, frankly," she said. "It was all about how Hillary is a real person. She has a belly laugh. She is a person of faith - things I didn't care about. I wanted to know about issues. They wanted to tell me what a fabulous human being she was."

Even so, the approach appeared to be working until the end of October, when Clinton made her first stumble in a campaign debate, hedging a question on immigration. In early December, a poll in the Des Moines Register gave Obama a slight lead in Iowa for the first time.

Obama's advantage - the poll gave him 28% to Clinton's 25 and Edwards's 23 - was statistically insignificant, being within the margin of error. But it was predictive. Clinton's double-digit lead in New Hampshire vanished, and Obama began to gain on her in the other early-voting state of South Carolina.

She has 12 days left to come back. If she does, in Iowa and New Hampshire, it will be because of her retuned political machine, and because of women such as Barbara Dennett, a mother of six and a schoolteacher from Newton, New Hampshire. "I just so believe in her for what she is doing for social concerns in this country," Dennett said. "I just want her to be a little more like me - in the peace movement. I want her to give us every reason to vote for her."

· Suzanne Goldenberg's book, Madam President: Is America Ready to Send Hillary Clinton to the White House? is available from guardianbooks.co.uk